# Non-Abelian Anyons and Topological Quantum Computation

@article{Nayak2008NonAbelianAA, title={Non-Abelian Anyons and Topological Quantum Computation}, author={C. Nayak and Steven H. Simon and Ady Stern and Michael H. Freedman and Sankar Das Sarma}, journal={Reviews of Modern Physics}, year={2008}, volume={80}, pages={1083-1159} }

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate… Expand

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#### References

SHOWING 1-10 OF 578 REFERENCES

Anyonic braiding in optical lattices

- Physics, Medicine
- Proceedings of the National Academy of Sciences
- 2007

This work explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice, and demonstrates how to detect the key feature of these excitations: their braiding statistics. Expand

Geometric phases and quantum entanglement as building blocks for non-Abelian quasiparticle statistics

- Physics
- 2004

Some models describing unconventional fractional quantum Hall states predict quasiparticles that obey non-Abelian quantum statistics. The most prominent example is the Moore-Read model for the… Expand

Towards universal topological quantum computation in the ν = 5 2 fractional quantum Hall state

- Physics
- 2006

The Pfaffian state, which may describe the quantized Hall plateau observed at Landau level filling fraction $\ensuremath{\nu}=\frac{5}{2}$, can support topologically-protected qubits with extremely… Expand

Topological Degeneracy of Quantum Hall Fluids

- 1997

We present a simple approach to calculate the degeneracy and the structure of the ground states of non-abelian quantum Hall (QH) liquids on the torus. Our approach can be applied to any QH liquids… Expand

Topologically protected qubits from a possible non-Abelian fractional quantum Hall state.

- Physics, Medicine
- Physical review letters
- 2005

Here, an experiment is proposed which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically protected qubit on which a logical Not operation is performed by qu asiparticle braiding. Expand

Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation

- Physics
- 2004

We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics… Expand

Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

- Physics
- 2006

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the… Expand

Quasiholes and fermionic zero modes of paired fractional quantum Hall states: The mechanism for non-Abelian statistics.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1996

The quasihole states of several paired states, the Pfaffian, Haldane-Rezayi, and 331 states, are studied, analytically and numerically, in the spherical geometry for the Hamiltonians for which the ground states are known exactly. Expand

Topological Quantum Computation

- Physics, Computer Science
- QCQC
- 1998

The connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions is explored and it is shown that if information is encoded in pairs of quasiparticles, then the Aharonov-Bohm interactions can be adequate for universal fault-Tolerance quantum computation. Expand

Quantum groups and non-Abelian braiding in quantum Hall systems

- Physics, Mathematics
- 2001

Abstract Wave functions describing quasiholes and electrons in non-Abelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this… Expand